p2+8p-77=0

Solution for p2+8p-77=0 equation:

p2+8p-77=0

We add all the numbers together, and all the variables

p^2+8p-77=0

a = 1; b = 8; c = -77;
Δ = b2-4ac
Δ = 82-4·1·(-77)
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{93}}{2*1}=\frac{-8-2\sqrt{93}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{93}}{2*1}=\frac{-8+2\sqrt{93}}{2}
$